Highlights• Auxiliary dipole method (ADM) optimizes TMS coil placement in under 8 minutes • Optimum orientations are near normal to the sulcal wall • TMS induced E-field is less sensitive to orientation than position errors Abstract Background: During transcranial magnetic stimulation (TMS) a coil placed on the scalp is used to non-invasively modulate activity of targeted brain networks via a magnetically induced electric field (E-field). Ideally, the E-field induced during TMS is concentrated on a targeted cortical region of interest (ROI).Objective: To improve the accuracy of TMS we have developed a fast computational auxiliary dipole method (ADM) for determining the optimum coil position and orientation. The optimum coil placement maximizes the E-field along a predetermined direction or the overall E-field magnitude in the targeted ROI. Furthermore, ADM can assess E-field uncertainty resulting from precision limitations of TMS coil placement protocols, enabling minimization and statistical analysis of E-field dose variability.Method: ADM leverages the reciprocity principle to rapidly compute the TMS induced E-field in the ROI by using the E-field generated by a virtual constant current source residing in the ROI. The framework starts by solving for the conduction currents resulting from this ROI current source. Then, it rapidly determines the average E-field induced in the ROI for each coil position by using the conduction currents and a fast-multipole method. To further speed-up the computations, the coil is approximated using auxiliary dipoles enabling it to represent all coil orientations for a given coil position with less than 600 dipoles.Results: Using ADM, the E-fields generated in an MRI-derived head model when the coil is placed at 5,900 different scalp positions and 360 coil orientations per position can be determined in under 15 minutes on a standard laptop computer. This enables rapid extraction of the optimum coil position and orientation as well as the E-field uncertainty resulting from coil positioning uncertainty.Conclusion: ADM enables the rapid determination of coil placement that maximizes E-field delivery to a specific brain target. This method can find the optimum coil placement in under 15 minutes enabling its routine use for TMS. Furthermore, it enables the fast quantification of uncertainty in the induced E-field due to limited precision of TMS coil placement protocols.